Graphical Abstract

Neutral Helium Atom Microscopy

Adria Salvador Palau, Sabrina Daniela Eder, Gianangelo Bracco, Bodil Holst

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Highlights

Neutral Helium Atom Microscopy

Adria Salvador Palau, Sabrina Daniela Eder, Gianangelo Bracco, Bodil Holst

• Research highlight 1

• Research highlight 2

Neutral Helium Atom Microscopy

Adria Salvador Palaua, Sabrina Daniela Edera, Gianangelo Braccob, BodilHolsta

aDepartment of Physics and Technology, University of Bergen, Allegaten55, Bergen, 5007, Norway

bCNR-IMEM, Department of Physics, University of Genova, via Dodecaneso33, Genova, 16146, Italy

Abstract

Neutral helium atom microscopy, also referred to as scanning helium mi-croscopy and commonly abbreviated SHeM, is a novel imaging technique thatuses a beam of neutral helium atoms as an imaging probe. The techniqueoffers a number of advantages such as the very low energy of the incidentprobing atoms (less than 0.1 eV), unsurpassed surface sensitivity (no pene-tration into the sample bulk), a charge neutral, inert probe and a high depthof field. This opens up for a range of interesting applications such as: imag-ing of fragile and/or non-conducting samples without damage, inspection ofnano-coatings, with the possibility to test roughness on the Angstrom scale(the wavelength of the incident helium atoms) and imaging of samples withhigh aspect ratios, with the potential to obtain true to scale height infor-mation of 3D surface topography with nanometer resolution. However, fora full exploitation of the technique, a range of experimental and theoreticalissues still needs to be resolved. In this paper we review the research in thefield. We do this by following the trajectory of the helium atoms step bystep through the microscope: from the initial acceleration in the supersonicexpansion used to generate the probing beam over the atom optical elementsused to shape the beam, followed by interaction of the helium atoms withthe sample (contrast properties) to the final detection and post-processing.We also review recent advances in scanning helium microscope design.

Keywords: Microscopy, SHeM, Molecular Beams, Helium Atom scattering,Neutral Helium MicroscopyPACS: 0000, 11112000 MSC: 0000, 1111

Preprint submitted to Ultramicroscopy December 28, 2021

1. Introduction

Neutral helium atom microscopes are surface characterisation tools thatapply a beam of neutral helium atoms as imaging probe. The instrumentsexploit a supersonic expansion of helium gas from a high pressure reservoir(100 bar range) through a nozzle into vacuum to generate a high-intensitybeam with a narrow velocity distribution, which is then collimated or focusedonto a sample. The scattered intensity signal is recorded “point by point”and used to create an image of the sample in a manner similar to other beamprobe microscopy techniques such as scanning electron microscopy or heliumion microscopy, but with the crucial difference that due to the very lowenergy1 and strict surface sensitivity of the neutral helium beam, the neutralhelium atoms scatter off the outermost electron density distribution of thesample. There is no penetration into the sample-material and no photons orsecondary electrons are generated during the scattering process.

Several abbreviations have been used for neutral helium microscopy overthe years, i.e. NEMI for NEutral MIcroscope [1], HeM for Helium Microscopeand NAM for Neutral Atom Microscopy [2], however the community nowseems to have agreed on SHeM for Scanning Helium Microscope, which wasactually also one of the first abbreviations, introduced by MacLaren andAllison already in 2004 [3]. We will use the abberaviation SHeM for the restof this paper.

The research behind neutral helium microscopes includes four main areas,which can be mapped to the different stages of the imaging probe trajectory.Firstly fluid dynamics, which is used to model the supersonic expansion ofhelium gas into vacuum and needed to establish the intensity and matterwave properties of the helium beam. Secondly, de-Broglie matter wave optics,which describes the interaction of the neutral helium atoms with the opticalelements, such as zone plates, pinholes and mirrors, critical for the microscoperesolution. Thirdly, helium atom surface scattering, modelling the interactionbetween the neutral helium atoms and the sample, thus determining the

1The energy of the helium atoms is determined by the temperature of the nozzle whichcan be cooled or heated. The energy range is typically between 20 meV correspondingto a de-Broglie wavelength of around 0.05 meV and 60 meV (room temperature beam)corresponding to a de-Broglie wavelength of around 0.05 nm, see equation 2. Helium atomswith energies in this range are referred to as thermal helium atoms, a term which is alsoused in this paper

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contrast properties. Finally the helium atom detection, targeting the difficultproblem of detecting hard-to-ionise neutral helium atoms. In addition tothese four area comes research specifically dedicated to the application ofscanning helium microscopes. This includes problems such as optimisation ofthe overall configuration of the tool, advanced imaging techniques (includingstereo-imaging), signal processing and image analysis.

For this review we have provided an open-source implementation of thesolution to the Boltzmann equation in spherical coordinates used in previ-ous helium microscope simulation work. It is meant as a service for thoseinterested in pursuing their own helium microscope designs. The code canbe found on GitHub: [4]. We also would like to draw the attention to the raytracing simulation program of the Cambridge SHeM, provided by Lambrickand Seremet, also available on GitHuB [5].

We begin this review with a brief historical overview of the research thatmade neutral helium microscopy possible. Then we follow the trajectory ofa helium atom through a neutral helium microscope as described above. Inthis way, we review the background research, step by step. Then we move onto discuss the latest research on microscope design and imaging techniquesand we present an overview of the SHeM images published up till now. Thepaper finishes with an outlook on the expected future of the field.

1.1. Some Background History

In 1930, one year before the electron microscope was invented, Estermannand Stern scattered an effusive beam of neutral helium atoms off LiF(100) andsaw diffraction peaks [6]. Their groundbreaking work had been made possiblethanks to previous work by Dunnoyer who established the first directed atombeam in 1911 [7].

The Estermann and Stern experiment did not instigate a new researchfield straight away, due to limitations in pumping technology which enabledonly the production of effusive beams, which have low intensity and a broadvelocity distribution (and therefore a broad de-Broglie wavelength distribu-tion). It took another twenty years for Kantrowitz and Grey to devise ahelium source with a narrower velocity distribution [8]. This was achievedthanks to a supersonic expansion of helium gas into a lower-pressure cham-ber (see Sec. 2.1). Notwithstanding the clear improvement that this brought,much narrower velocity distributions and higher intensities were imperativefor the success of neutral helium atoms as a scattering probe.

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Such beam properties were achieved in the early 1970s thanks to theimprovement of vacuum techniques and the introduction of small nozzles,which allowed for supersonic expansion into ultra high vacuum. The centralpart of the beam was selected using a conically shaped aperture, a so calledskimmer - until that point, slits had been preferred. By the 1980s, nozzletechnology had advanced so much that the velocity distribution of the heliumbeams had become narrow enough that the small energy changes2 resultingfrom the creation or annihilation of surface phonons could be measured [9].This propelled helium atom scattering as a method suitable to study surfacedynamics [10, 11, 12, 13].

Eventually, physicists began to speculate on how the surface sensitivityof helium could also be used to construct an imaging instrument. It soon be-came clear that focusing optics was a particular challenge. Neutral, ground-state helium has the smallest polarisability of all atoms and molecules. Hencemanipulation via electrostatic or electromagnetic fields is essentially not pos-sible. Furthermore, helium atoms at thermal energies do not penetrate solidmaterials. In practice, the only possible way to manipulate them is via theirde-Broglie matter-wave properties. This leaves only three possibilities: sim-ple collimation, focusing via mirror reflection or focusing via diffraction fromfree-standing structures (zone plates).

To the best of our knowledge, the first mentioning in the official scientificliterature of the idea of a neutral helium microscope was in 1989 when Doakdemonstrated focusing in 1D by reflecting a neutral, ground state heliumbeam off a mechanically bent, gold-coated piece of mica [14]. In 1991 Carnalet al. presented the first experiment on 2D focusing of neutral helium beams:The focusing of a beam of metastable helium atoms using a Fresnel zoneplate [15]. In 1997 Holst and Allison achieved astigmatic focusing in 2D byscattering a neutral, ground state helium beam off a Si(111)-H(1x1) surfaceelectrostatically bent to a parabolic shape [16]. The silicon wafer used hada thickness of 50 µm. The area of least confusion had a spot diameterof 210 µm, which Holst et al. used in a later experiment to image theionisation region of an electron bombardment detector [17]. In 1999 Grisentiet al. obtained the first focusing of neutral, ground state helium with a zoneplate. They used a micro skimmer as a source and achieved a focused spotdiameter of less than 2 µm [18].

2meV range.

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In 1999 it was proposed that by changing the boundary conditions fromround to ellipsoidal a mirror without stigmatic error could be obtained byelectrostatic bending [19], see also [20, 21, 22]. In 2010 Fladisher et al.achieved near stigmatic focusing of helium atoms using this method [23].Despite work on the optimisation of the hydrogen passivation of the Si(111)surface [24] and the development of a transport procedure that allowed trans-port of mirrors to microscope systems [25], it remained a problem with theSi(111)-H(1x1) mirrors that there is a considerable loss in intensity in thespecular beam due to diffraction from the corrugated electron density distri-bution at the surface [26, 27, 28]. In 2008 Barredo et al. showed that thereflectivity of an atom mirror could be dramatically improved by coating thesilicon wafer surface with a 1-2 nm layer of lead [29]. This so called-quantumstabilised mirror demonstrated a specular helium reflectivity of 67%. In alater work Anemone et al. explored the use of flexible thin metal crystals asfocusing mirrors [30], following an early attempt from 1999 [22].

Despite the promising achievements in bent mirror focusing, the problemremains that to achieve focal spots at the nanometer range, near uniformlyflat crystals without warp are necessary. Work has been done on thin wafercharacterisation targeted for atom mirror applications [31, 32] and on howwafer imperfections identified through this characterisation can be compen-sated for by a multiple electrode structure for bending [33], but even sotechnological requirement seems to have put an end to research on the cre-ation of focusing atom mirrors through thin crystal bending, at least for thetime being.

An alternative path for making atom focusing mirrors without thin crystalbending was proposed in 2011 by Sutter et al. who showed that a high-reflecting mirror with a specular helium reflectivity of 23% could be obtainedwith a graphene-terminated Ru(0001) thin film grown on c–axis sapphire [34].Earlier work had shown that monolayer graphene can grow on polycrystallineRu thin films on arbitrarily shaped surfaces [35], this in principle, paves theway for making a focusing mirror by growing a thin layer of ruthenium on asapphire substrate polished to the desired mirror shape. Work pursing thisis ongoing [36].

The first SHeM image was obtained by Koch et al. in 2008 [37], see Fig. 1.Koch et al. obtained a 2D shadow image of a free standing grating structurewith a resolution of around 2 µm using a micro-skimmer (see section 6.1) anda Fresnel zone plate to focus the helium beam onto the grating, a diagramof the instrument can be seen in Fig. 2. The best SHeM resolution obtained

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Figure 1: First SHeM image. The image is a 2D shadow image, showing a free standinggrating structure. The image is obtained by scanning the focused beam across the sample,recording the signal from the transmitted helium atoms, see Fig. 2. Image reproducedfrom [37].

with a zone plate up till now is slightly less than 1 µm, demonstrated by Ederet al. [38]. This is very far from the theoretical resolution limits which arediscussed in section 3. Note that for the zone plate microscope configuration,the 0-order component of the beam should be retained in order to minimizethe background signal. This can be done using a so called order-sortingaperture, also known from X-ray optics. An order sorting aperture for heliumfocusing with a zone plate was demonstrated in [39]. In 2008 a zone platewas also used by Reisinger et al. to focus a beam of deuterium molecules,as a first demonstration of the potential of making microscopes with otheratomic and molecular beams [40], see also [41]. For a description of the zoneplates used for neutral helium microscopy see [42, 43, 44, 45] .

After the work of Koch et al., other research groups focused on a simplerconfiguration: the pinhole microscope. This configuration uses a small cir-cular aperture (a pinhole) to collimate the beam instead of focusing optics.

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Figure 2: Diagram of the first SHeM microscope used to obtain the image shown in Fig. 1.The beam is generated by a free-jet (supersonic) expansion through a micro-skimmer (seesection 6.1) which is imaged onto the sample plane by the zone plate’s plus first diffractionorder. In addition, the zero as well as the minus first order are indicated. s is the sourceto zone plate distance and s’ the distance from zone plate to image plane. The indicatedaperture just serves to filter background from the source. The sample is scanned acrossthe beam by a piezo table. The transmitted intensity of the beam is recorded at the backto obtain an image in transmission mode. This first SHeM microscope did not have anorder-sorting aperture [39]. Figure reproduced from [37].

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The resolution is determined by the size of the pinhole, see Fig. 4. Withthis configuration Witham and Sanchez managed to obtain the first SHeMimages in reflection mode in 2011 [2], see Fig. 3. The initial resolution was1.5 µm and later 0.35 µm [46], which remains the highest resolution obtainedso far with a neutral helium atom microscope. In 2014 Witham and Sanchezalso demonstrated reflection imaging with a Krypton beam [47]. Around thesame time as Witham and Sanchez other researchers had started working onpinhole microscopes with a different design, using a skimmer in combinationwith a collimating pinhole aperture [48]. The first images from this typeof instrument were published by Barr et al. in 2014 [49]. For a diagramof the setup, see Fig. 5. The advantage of this new pinhole design is thatthe perturbation of the helium atoms trajectories through backscattering isstrongly reduced by using a skimmer, see for example [50] and section 2.2.3.This means that the new pinhole design should have an increased intensityin the beam spot on the sample and provide a narrow, well defined velocitydistribution. The latter is of particular interest for contrast properties, seesection 4. A counter argument in favour of the first design is that here thepinhole can be brought closer to the nozzle, which in principle should also in-crease the intensity. No detailed comparisons between the two designs havebeen presented in the literature up till now. At present it seems that thecommunity mainly pursues the second design. To this day, the pinhole setupremains the most widespread neutral helium microscopy design, despite thefact that higher resolution can be achieved with the zone plate configurationas will be discussed in section 6.

2. The Helium Source

In a SHeM atoms start their journey in the source. A typical SHeM sourcefollows the design established for helium atom scattering (HAS) [51, 48, 49]:helium is accelerated in a supersonic expansion from a high pressure reservoirthrough a de-Laval nozzle3, into a vacuum chamber, known as the expansionchamber [52]. There, the central part of the beam is selected by a conicallyshaped aperture, called the skimmer4.

3Often the nozzle is cut in the sonic plane, and is referred to as a sonic nozzle [52]4Some designs skip the skimmer altogether and use a single collimated aperture far

downstream [2]

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Figure 3: First SHeM image obtained in reflection mode. The image shows an uncoatedpollen grain on a Quantifoil grid. The image is created by detecting the atoms scatteredat a particular angle, image reproduced from [2].

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Figure 4: Diagram of the first pinhole SHeM. Figure reproduced from [2]

Figure 5: Schematic diagram of the second pinhole SHeM using a skimmer in combinationwith a pinhole. The helium beam is generated in a free-jet (supersonic) expansion in thesource chamber (1), passing through a differential pumping stage (2) to the pinhole optics.The collimated beam hits the sample in the sample chamber (3). The scattered heliumentering the detector chamber (4) where it stagnates to form a stable pressure, whichis measured. The image is produced by scanning the sample under the beam. Figurereproduced from [49]

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Figure 6: Schematic diagram of a free-jet (supersonic) expansion. The source expandsfrom a helium reservoir with pressure P0 and temperature T0 through a nozzle of diameterd into a vacuum. The Mach number M (ratio of flow velocity to the local speed ofsound) rapidly increases during the initial expansion. As the expansion continues thereis a transition from continuum flow to molecular flow, which is often modelled with theso-called ”quitting surface” (see Fig. 7). The central part of the beam is sampled by taskimmer. In modern, high-efficient pumping systems the position of the Mach disc is oftenbehind the skimmer and for low background pressure the shock structure and Mach discare less pronounced and disappear. Figure reproduced from [48]

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When designing a Helium Source, one can essentially choose five param-eters: temperature, pressure, nozzle radius5, skimmer diameter and distancebetween skimmer and nozzle6. In general, small nozzles and high pressuresproduce brighter7 sources and therefore are more efficient in reducing unde-sired effects such as back-scattering interference (as the beam is more focused,if the same flow is assumed, less particles are emitted at undesired angles)[54, 55]. Similarly, cold sources are more intense than warm sources andproduce higher parallel speed ratios8 [51, 50], which allows them to reachhigher centre-line intensities. The absolute differences between a cold (liquidnitrogen cooled) and a warm source at the same pressure can easily be onthe order of 1 · 1013counts/s ·m2 [50].

Once the nozzle size and temperature have been chosen, obtaining thebeam properties corresponds to (i) solving the supersonic expansion of theHelium gas into vacuum, and (2) calculating the beam intensity after theinitial expansion. This chapter is structured with these two steps in mind:first, we discuss the work done on describing the supersonic expansion, andthen we discuss the different models that give the beam intensity downstream.

2.1. The supersonic or free-jet expansion

As mentioned above the first component of a helium source is the nozzle,where atoms are accelerated to supersonic speeds in a physical phenomenonknown as a supersonic expansion.

The theory describing supersonic expansions was developed in the 1970sand 1980s, and is based on splitting the expansion into two regimes: the firstregime, within the nozzle, follows a Navier-Stokes flow, and is solved throughthe isentropic nozzle model [7, 56]. The second regime, from the nozzle exitonward, is modelled through the Boltzmann equation. The flow is obtainedeither by solving the corresponding integrals under simplifying assumptions[57, 58] or using Direct Simulation Monte Carlo (DSMC). [59, 60, 61].

5The issue of nozzle design is left as outside of the scope of this paper. For a discussionof this topic see for example [53, 52].

6There are also important considerations that needs to be done regarding vacuumchamber design, required pumping speed etc., but that is beyond the scope of this paper

7Count rate per steradian and unit area of the source.8The speed ratio of a supersonic molecular beam is defined as v

∆v where v is the mostprobable velocity and ∆v is the Full Width at Half Maximum of the velocity distribution.

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2.1.1. The isentropic nozzle model

Within the nozzle, the helium gas density is high (typically up to 200 bar)and the flow is modelled with Navier Stokes equations. The isentropic nozzlemodel gives the total flux per unit time (from now on, centre line intensity)stemming from a de Laval nozzle (assuming that the nozzle is cut-off in thesonic plane). This derivation considers an ideal gas in which the flow can beassumed to be a reversible and adiabatic process. Therefore the gas can beconsidered isentropic - which means that the following analytical equation ofthe intensity can be obtained [7].

I0 =P0

kBT0

√2kBT0

m

(πr2

nz

)√ γ

γ + 1

(2

γ + 1

)1/(γ−1)

, (1)

where T0, P0 are the temperature and the pressure in the source. rnz is theradius of the nozzle and m is the mass of a helium atom. γ is the heatcapacity ratio (γ = 5/3 for helium), and kB is the Boltzmann constant. Onecan also obtain the terminal velocity, v, which can be used to provide themost probable de-Broglie wavelength of the atoms in the beam: [7]:

v =

√5kBT0

m. (2)

This model is used to calculate the total flow from the nozzle - as itis well known that helium is the closest we get to an ideal gas [62]. Somegroups also choose to add a correction given by the thickness of the boundarylayer in a real gas. Beijerink and Verster provide a correction factor fora monoatomic gas [52]. To our knowledge, all helium microscopy papersmodelling the intensity of the helium beam use an initial intensity derivedfrom the isentropic nozzle model (see Sec. 2.2.2 for a breakdown).

2.1.2. Post-nozzle flow

Once the helium atoms have left the nozzle, the pressure drops and theflow is governed by the Boltzmann equation - as the Navier Stokes equationscease to apply. There are two main methods to solve the flow: either bynumerically solving the Boltzmann equation under stringent assumptions[63, 64, 7] or by simulating the particle flow using DSMC. The latter methodis more computationally intensive, but also more accurate than the formeras it relies on fewer assumptions: For the first method, one typically assumesthat the nozzle is a point source [57]. This assumption is grounded on work

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from Sherman and Ashkenas, which showed that a few nozzle diametersdownstream, free jet streamlines become straight and can be extrapolated toa single point of origin close to the nozzle [63, 64]. The flow then can be solvedusing the collision integral for particles following Bose-Einstein statistics.The isentropic nozzle model at a short distance from the nozzle is used toobtain the initial conditions to start the integration9. To solve this equation,a velocity distribution, and an interaction potential have to be assumed.The equations needed to solve the expansion are included in [50, 7]. Asmentioned above for this review, we provide an open-source implementationof the solution to the Boltzmann equation in spherical coordinates [4].

The velocity distribution of the atoms is taken to be an ellipsoidal Maxwellian:

fell (~v) = n

(m

2πkBT||

) 12(

m

2πkBT⊥

)· exp

(− m

2kBT||(v|| − v)2 − m

2kBT⊥v2⊥

).

(3)The choice of an ellipsoidal Maxwellian velocity distribution forms the

basis to solve the spherically symmetrical Boltzmann equation [65]. In thesemodels, the expansion’s macroscopic properties are expressed in a spheri-cal coordinate system. The temperature is split in two terms, modellingthe velocity distributions of the radial and angular component of the ve-locity in spherical coordinates v‖ and v⊥: T|| and T⊥. These are propor-tional to the variance of the velocity in that coordinate system, for exampleT|| =

mkB〈(v|| − v0

||)2〉, where v0

|| is the parallel component of the mean velocityvector. v is the most probable velocity of the beam along the radial direction.n is the number density of atoms.

On top of the assumption regarding the velocity distribution of the atoms,an interaction potential must be assumed. There are several options forthis potential: the Lennard-Jones potential [66], the Tang, Toennies andYu (TTY), and the Hurly Moldover (HM) potentials [67, 68] being amongstthe best known. Results of previous calculations show that the Lennard-Jones potential is accurate for source temperatures as low as 80 K [69, 70].Therefore, this is often the preferred choice by practitioners in the field asthe Helium source is rarely cooled below this temperature [69, 70, 71]. A

9This is a rather arbitrary distance that must be large enough to guarantee spheri-cal symmetry and small enough to satisfy equilibrium conditions, typically a few nozzlediameters.

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detailed description of the Lennard-Jones potential and its implementationin the Boltzmann equation can be found in [71].

The numerical solution of the Boltzmann equation in its spherical approx-imation provides the evolution of the average gas velocity, and the tempera-tures T|| and T⊥ with respect to the distance from the nozzle. This solutioncan then be used to determine the intensity of the beam at the sample planeby means of the so called quitting surface model - see Sec. 2.2.1. This solu-tion can also be used to obtain the velocity distribution and speed ratio of thebeam. These have been shown to be in good agreement with experimentaldata [51].

As mentioned above an alternative way of solving the Boltzmann equa-tion, requiring less assumptions, is to directly simulate particle-to-particleinteractions using DSMC [60, 59]. This method addresses the numericalinfeasibility of simulating the flow particle by particle by grouping thoseparticles onto pseudo-molecules that are taken to represent a larger groupof real molecules. DSMC requires assumptions on the interaction of thepseudo-molecules with the surface and with each other. These are normallyphenomenological models such as the hard sphere model [59], the variablehard sphere model [72] and others [73]. DSMC is truer to nature than solv-ing the Boltzmann equation under stringent assumptions but is also muchmore computationally expensive. Several papers have used this method tounderstand the behaviour of the helium expansion [74, 61, 75].

2.2. Intensity after the initial expansion

As the helium atom travels further away from the nozzle, it interacts lessand less with neighbouring atoms. This means that modelling the supersonicexpansion all the way to the sample plane is numerically inefficient.

Therefore, theorists often choose to use the fact that the Knudsen numberof the flow increases with distance to the source, and that quasi-molecularflow is often reached before the first optical element, usually the skimmer, tobuild simplified models of the intensity. Quasi-molecular flow allows for therecovery of analytical expressions of the centre-line intensity, as particles canbe assumed to travel in a straight line without further interactions.

Over the years, several intensity models have been proposed for heliumsources. A combination of arbitrary variable labelling, numerical simplifi-cations and empirical formulae has left researchers with no unified intensitymodels. The landscape is confusing, and in this paper we make an attempt

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to unify and simplify the different intensity models and explain how theycompare with each other.

We propose the following geometrical conventions: consider always anexpansion stemming from a nozzle, followed by a skimmer. The skimmer isplaced at a distance xS from the source of the supersonic expansion with noother apertures in between. Take a as the distance between the skimmer andthe axial point in which the intensity is measured. The distance betweenthe nozzle and the measuring point is then (xS + a). All the rest of physicalvariables correspond to those presented in Section 2.2.1.

We propose that the intensity should always be given as particles persecond per unit area10. On top of this, the intensity can be assumed to beslowly-varying enough that to obtain a total intensity hitting a detector itis enough to multiply the centre-line intensity by the detector’s area. Themedley of analytical formulas found in literature can be confusing, but fol-lowing this convention one sees that they all have a common factor. Overall, there are three families of intensity models: those that treat the nozzleas a source of a spherically symmetric flux, and account any excess inten-sity by using an empirical factor [52], those that on top of this consider thethermal properties of the supersonic expansion through a dependency on thebeam’s speed ratio, and those that explicitly integrate the quitting surface11

under some assumptions. All three families of intensity models are faulty asthey rely on overly simplistic assumptions, but they are also useful in thatthey provide an analytical expression for the intensity. We start in the nextsection by considering the third family.

2.2.1. The quitting surface intensity model

One of the most popular intensity models relies on the quitting surfacemodel [57, 76, 50] with the associated definition ”virtual source”. A quittingsurface12 is a useful theoretical construct which assumes that at a givenpoint in the beam’s supersonic expansion, particles start travelling in straightlines. This point is defined through asymptotic conditions on the properties

10We chose unit area over steradians to signify the departure from spherical symmetrytypical of supersonic beams.

11Or an equivalent concept - known as the virtual source [54]12Also referred to as “last collision surface” [52, 77].

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Figure 7: Schematic diagram of a supersonic expansion and definition of the virtual source.Figure reproduced from [71]

of the expansion; either as the point in which the Mach number13 of theexpansion approaches its predicted terminal Mach number [2, 78] or as thepoint in which the parallel and perpendicular temperature of the Maxwelliandistribution used to model the expansion decouple [79].

The main utility of this model is that the intensity and velocity distri-bution of the beam can be obtained by integrating this spherical particle-emitting surface. This distribution can then be backtraced from the quittingsurface to a so called virtual source plane, which describes the intensity andvelocity distribution that a source would need to have to give rise to theobserved distribution at the quitting surface. The virtual source plane istaken as the plane where the spatial distribution has the minimum exten-sion. This means that the virtual source can be viewed as the object thatwith a view reduced by the skimmer, is imaged onto the sample plane by thezone plate in the zone plate microscope. Zone plates have actually been usedin combination with large skimmers to obtain direct images of the supersonicexpansion [71, 41, 80]. The difficulty associated with this method is the rela-tive arbitrarity of the definition of the quitting surface, which depending on

13Ratio of flow velocity to the local speed of sound, see [64] for a discussion in thecontext of atom beams.

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the condition chosen, can be positioned before or after the skimmer aperture.As mentioned above, the quitting surface can be integrated to obtain an

analytical model for the beam intensity: the Sikora approximation [57]. Thisexpression was initially calculated for a quitting surface placed exactly atthe skimmer aperture and was later generalised by Bossel to incorporate aquitting surface placed before the skimmer [58]. This formula was used, quitesuccessfully to model experimental measurements of centre line intensities[50] and is used in the first two papers by Salvador et al. on optimisation ofpinhole and single zone plate helium microscope configurations [81, 76]:

IS = ITG

{1− exp

[−S2

i

(rS(RF + a)

RF(RF − xS + a)

)2]}

, (4)

where xS is the distance between the nozzle and the skimmer and a is thedistance between the skimmer and the point where the intensity is measured.rs is the radius of the skimmer and RF is the radius of the quitting surface.The first term of the Sikora approximation ITG is the intensity correspondingto a naive spherically-symmetric model of the supersonic expansion, wherethe atoms would travel in straight lines from the nozzle with equal probabilityat any angle and no thermal effects14. The total flow stemming from thisideal point source corresponds to the intensity resulting from the isentropicsource model I0. We name this factor the thermal-geometrical component,ITG. The thermal-geometrical intensity measured at a detector of radius rDis then:

ITG = πI0r2D

(xS + a)2. (5)

This component suffices to understand a basic design principle of neu-tral helium microscopy: reducing the axial length of the microscope is oftenbeneficial, as intensity will decrease with distance.

The second term of the Sikora equation, the exponential term, modelswhat we may term the thermal properties of the beam. The Si there indi-cates that depending on the microscope design the perpendicular (⊥) or the

14The density at the skimmer can also be used, if the point source assumption is dropped[50].

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parallel (||) speed ratio dominates:

Si =

√mv2

2kTi, i = ||,⊥. (6)

Here, Ti corresponds to the perpendicular or parallel temperature (as definedin eq. (3)). In general, for small skimmers close to the quitting surface, usingthe parallel speed ratio in the Sikora model reproduces experimental mea-surements better (as perpendicular spread is not a big contributor given thatvery little of the quitting surface is seen at the detector). However, for largerskimmers seeing a thermalised portion of the expansion (for example, whenthe expansion is not assumed to end until significantly after the skimmer)the perpendicular speed ratio dominates [50].

As mentioned above, the thermal-geometrical term ITG describes a spher-ically symmetrical expansion. In reality as supersonically expanded atombeam decreases in intensity at a slower rate than a spherically symmetricalexpansion. Thus the full Sikora-Bossel equation ( eq. 4) gives a truer de-scription of the phenomena at play. Let us look at this equation in the smallskimmer limit:

IS = ITG

{S2i

(rS(RF + a)

RF(RF − xS + a)

)2}

(7)

For a quitting surface at the skimmer RF = xS we get:

IS = ITG

{S2i

(rS(xS + a)

axS

)2}

= ITG

{S2i

(rS

a+rS

xS

)2}

(8)

This equation adds three important (and physical) corrections: (i) the beamwill be more intense the wider the skimmer is - which accounts for thermalcomponents of the quitting surface. (ii) Higher speed ratios means moreintense beams - which is a measure of the quality of the supersonic expansionand of its departure from a spherically symmetrical expansion. (iii) the closeryou are to the beam source, the more intense the beam will be. Note that (i)is still an approximation and only holds for small skimmers - if the skimmersize is on the order of the size of the quitting surface, increasing it furtherdoes not result in important intensity changes. The fact that the beamintensity decreases slower than in the spherical case, has design implications.

19

It allows for larger and hence technologically more feasible microscopes. Itis important to be aware of this when doing SHeM designs (see section 6).

2.2.2. Other intensity models

Rather than integrating over the quitting surface/virtual source as de-scribed in the previous section one can obtain analytical expressions for thecentre line intensity by using various additional approximations. In this sec-tion we review other intensity models that have been used for SHeM andshow how they compare to the isentropic, spherically symmetric expansionmodel, expressed by the thermal-geometrical term, ITG (see eq. 5). Themodels that have been used for SHeM so far, have been inspired by centreline intensity derivations of Pauly [7], Miller [56] and dePonte [54] as well asSikora (described above)

We start with models from the first family as described above, to whichboth Pauly and Miller belongs. These models approximate the intensityby considering a simple flow pattern: an isotropic15 spherically symmetricexpansion - such as what is assumed to obtain ITG. The expression for thecentre line intensity presented below is used to describe SHeM among othersby [1, 82]. Note that the expression differs from Pauly’s calculation by afactor of approximately 2. We think that this is a missing factor carried onfrom Miller’s nozzle intensity model [56].

I = 0.155P0

kBT0

(2rnzxS + a

)2πr2D

√5kBT0

m= 0.62

√5/2

I0

f(γ)

r2D

(xS + a)2= 0.6077ITG

(9)Secondly, we look at the expression used by Witham and Sanchez [2] to

estimate the intensity in their pinhole microscope (see Fig. 4). Withamand Sanchez explicitly refer to Miller’s derivation [56] for an isentropic in-tensity. As mentioned above, Miller’s result for I0 differs from the derivationpublished by Pauly (eq. 1) [7] by one half.

Witham and Sanchez correct for the excess intensity from the supersonic

15Note that isotropic is not the same as isentropic. Isotropic refers to the intensity beingindependent of the direction (spherically symmetric). Isentropic refers to the thermody-namic properties of the flow within the nozzle.

20

expansion in the beam direction by using a peaking factor κ.

I = κP0πr

2nz(

γ−12

+ 1)γ/(γ−1)√

γkBT0

m

kT0

πr2D

(xS + a)2

≈ 0.4871 ∗ 2κ√γ/2

I0

f(γ)

r2D

(xS + a)2≈ 1.1026ITG. (10)

Where f(γ) =√

γγ+1

(2

γ+1

)1/(γ−1)

≈ 0.5135. Here κ is the peaking factor,

obtained numerically by calculating the flow after the aperture and com-paring it with the equation above. κ has been empirically measured to beapproximately 2 for monoatomic gases [52]. γ = cp/cv is the heat capacityratio, which is 5/3 for monoatomic gases. rnz is the radius of the nozzle.

Note that both these equations do not include the skimmer radius. Inthe case of Witham and Sanchez this makes sense since they are modellinga microscope design that does not include a skimmer, however, experimentshave shown that in systems with a skimmer, the size of the skimmer has tobe considered [50].

Finally in [83] Bergin et al. model the source in a helium microscopeusing DePonte et al’s centre-line beam intensity (with a correction) [54, 83].This is a model of the second type, in which an empirical formula for thedependency between the virtual source radius and the speed ratio of thebeam is used (and therefore an inverse dependency on the speed ratio isintroduced). Bergin et al. use the following formula (in flux per unit area):

Iberg = πβ2B = π

(rS

xS + a

)2

B. (11)

Where B is the brightness of the source (in number of atoms per steradianper unit area of the source). Bergin et al. provide an expression for B:

B = 0.18P0

S||√mkBT0

. (12)

Combining both equations Bergin et al. arrive to a similar quadraticdependency with the skimmer radius as Sikora does in the limit of smallskimmers. Once rewritten in terms of ITG and multiplied by πr2

D the intensity

21

arriving at a detector downstream is recovered:

I =0.18π2P0r

2S√

mkBT0

r2D

S||(xS + a)2=

1

S||

0.18π√2f(γ)

I0

r2nz

r2Sr

2D

(xS + a)2≈ 0.247866

S||

(rSrnz

)2

ITG.

(13)Here, rS is the radius of the skimmer. Note how all three models have thesame geometrical dependencies stemming from a spherically symmetrical ex-pansion: the ITG term. The intensity is then corrected upwards or downwardsdepending on further assumptions.

2.2.3. Skimmer effect

The intensity models discussed in the last section disregard any effectproduced by the skimmer besides acting as an aperture. However, the realityis that skimmer interference is often a significant contributor to the beam’scentre-line intensity [50]. In its journey, a helium atom can see its trajectoryperturbed by atoms backscattered from the skimmer, or more generally aperturbation of the flow caused by it.

Modelling the effect of the skimmer is a well known challenge in heliumbeam experiments [55, 53, 62]. One of the most successful approximations tothe problem is the one provided by Bird in the 1970s [61]. In this paper, Birdproposed the modified Knudsen number, and showed it to be a better pre-dictor for skimmer interference than the Knudsen number. When designinga microscope, one should always aim for a modified Knudsen number largerthan 1, as skimmer effects can decrease intensity by a factor of as much as10 times [50]. The modified Knudsen number for a Lennard-Jones potentialreads:

Kn∗ = Kn

(2

5S2||

)−1/6

=1

rSσ√

2n

(2

5S2||

)−1/6

. (14)

In here, the speed ratio term does not have any other effect than reducingthe effective Knudsen number with respect to the normal Knudsen number.For a skimmer placed at a given distance xS from the expansion, the truedominant factor is the skimmer radius rS - smaller skimmers give largerKnudsen numbers. σ is the scattering cross-section of the atoms and n is thenumber density. The Knudsen number can be easily approximated by theexpression above and one can obtain the conditions in which the skimmer iswell conditioned. In general, if one wants to control the optical propertiesof the beam, one must place the skimmer as close to the quitting surface as

22

possible whilst having a radius that leads to a large enough modified Knudsennumber.

Since the introduction of the modified Knudsen number and the DSMCcalculations by Bird there have been several attempts at modelling skimmerinterference without flow dynamics simulations. One of the attempts thatmanaged to replicate experimental data the best was a numerical model byHedgeland et al. [55]. In their paper, the authors propose that skimmerattenuation is mostly caused by the collision of backscattered particles withthe central axis of the beam and provide a model to explain what they call an“anomalous attenuation” of the beam at low temperatures. The advantageof this model is that the backscattered atom’s cross section can be obtainedfrom the solid angle of the beam and a series of assumptions on the natureof the He-He collisions. This improves on previous attempts that dependedon parameter fitting [62].

Although this model is very promising and replicates well the experi-mental data reported by [55], it also predicts an inverse dependency of theatom’s cross section with the solid angle of the beam. This means that thecross section would decrease for bigger skimmers (that are known to pro-duce broader beams). However measurements published in 2018 [50] showthat larger, equally streamlined, skimmers actually produce more interfer-ence than small skimmers - as predicted by the Knudsen number [50]. Thesenew measurements cannot be explained by Hedgeland et al.’s model. Thus,it seems that researchers are still left with no other option than to model thefull interference of the beam with the skimmer if they want to obtain precisepredictions of the skimmer effect.

2.2.4. Other effects

In addition to skimmer interference, helium atoms can interact with atomsscattered from any other element of the expansion chamber (also known asthe background gas). Such interactions depend on the vacuum quality (pumpcapacity and in the case of a pulsed beam, size of the vacuum chamber) andcan be modelled either through DSMC or through free molecular scattering.The latter is often preferred as it corresponds to a simple exponential law[55, 62, 50]:

I

IS= exp

(−σ2nBExS − σ2nBCa

)(15)

Where σ is the scattering cross-section of the atoms and nBE and nBC arethe background number densities in the expansion chamber and subsequent

23

chamber. These background densities should be measured by a pressuregauge far away from the beam centre line.

3. Helium optics / Resolution limits

Once the centre line of the supersonic expansion has been selected bya skimmer, the helium atoms continue to travel in straight lines throughvacuum until they interact with the microscope optical elements.

In this regime, the behaviour of helium atoms can be modelled by atomoptics through the wave-particle duality. The wavelength, and thereby theresolution, is given by de-Broglie wavelength equation [84]: λB = h

p= h√

2Em.

The mass of Helium is about four orders of magnitude higher than the elec-tron mass. Thus, at the same energy, the de-Broglie wavelength of neutralhelium atoms will be two orders of magnitude smaller than of electrons andthus the potential resolutions two orders of magnitude better. According toeq. (2) a room temperature helium beam has a wavelength of around 0.05 nmand an energy of 50 meV [12]. A beam cooled with liquid nitrogen and work-ing at 120 K has a wavelength of around 0.1 nm and an energy of around20 meV. However, the practical resolution limit of a Helium microscope con-figuration is not given by the theoretical wavelength limit, but by aberrationand diffraction (Airy disk) broadening by the optical elements. As discussedin the introduction, two types of optical elements have been used so far tosuccessfully produce SHeM images: Fresnel zone plates and pinholes. Fresnelzone plates are a type of diffraction lens that focuses an incoming atomic orlight beam into a small focal spot [15]. Pinholes are circular openings thatrestrict the size of the atom beam [2].

When referring to resolution, it is important to distinguish between thelateral resolution, determined by the size of the helium beam, and the “angu-lar resolution”, given by the solid angle covered by the detector opening. Thelateral resolution is what impacts the minimum feature size that can be ob-served and therefore is referred to in the field as “resolution”. Diffraction withdetecting apertures does not degrade the lateral resolution as in light optics,because helium microscopes image by measuring the flux through the aper-ture and not by projecting the image onto a sensor plane. Angular resolutiondetermines the intensity of scattered helium in a particular direction. Thisis mainly of relevance for contrast, in particular for 3D imaging, as multiplescattering makes it difficult to image high aspect ratio structures [85, 86].

24

In 2018 the concepts supra- and sub-resolution were introduced to heliummicroscopy [87]. Supra resolution is the same as the lateral resolution, deter-mined by the size of the helium beam. Sub-resolution refers to the fact thatthe wavelength of the helium atoms may introduce a contrast effect. Thiswill be discussed in more detail in section 4.

The difference between the resolutions of Fresnel zone plates and pinholemicroscopes is given by the contributions of diffraction (Airy disk) and aber-ration terms [88]. The square of the Full Width at Half Maximum16 for thezone plate (ΦZP) and the pinhole (ΦPH) microscope can be written as:

Φ2PH = O2

S + σ2A (16)

Φ2ZP = O2

S + σ2A + σ2

cm. (17)

Where O2S indicates the geometric optics contribution to the full width half

maximum. That is to say O2S is the image of the source at the sample. For

the zone plate microscope it is the demagnified image of the skimmer orthe source limiting aperture [89], σA is the Airy disk contribution from edgediffraction from the zone plate or pinhole and σcm is a chromatic aberrationterm that appears for the case of the zone plate. The first equation holdsunder the assumption that the Fresnel number is smaller than 1, which isthe case for the limit of small pinholes. For a Fresnel number larger than 1only the geometric optics term plays a role [81].

Besides the de-Broglie wavelength, there is no theoretical limit as to howsmall OS can get. However, for the case of a pinhole, σA grows as 1/rph ∝1/OS [81], thus the Airy term increases when one tries to decreaseOS. For thezone plate the situation is more complex, because of the additional chromaticaberration caused by the velocity spread of the helium beam. The chromaticaberrations in a zone plate are proportional to its radius, while its Airy termdepends linearly with ∆r: σA ∝ ∆r ∝ OS. [76]. In other words, for a fix zoneplate radius both the resolution and the Airy contribution decrease linearlywith the same factor. This allows zone plates to reach significantly higherresolution (smaller spot size) than pinholes [76, 83], see also section 6.

The resolution limits for both instruments can be explicitly obtained (see

16The full width at half maximum of the beam’s intensity profile [81].

25

[81, 76]). For a pinhole microscope:

ΦminPH = K

√0.42λWD

√3. (18)

Where K = 2√

2 ln 2/3 and WD is the working distance (the distance be-tween the optical element and the sample). The 0.42 factor comes from theAiry disk standard deviation [90]. In a zone plate microscope the minimumpossible resolution (minimum size of the focused spot) is given by the widthof the smallest zone (as the optical and Airy terms both linearly depend on∆r).

ΦminZP = KσA ≈ ∆r. (19)

This is a well-known result from light optics for the first order focus [88].For higher orders the focused spot size can be smaller than the width ofthe smallest zone [88]. This sounds promising at first, but given that onlya fraction of the beam enters into the focus (max 12.5% for the first orderfocus and much less for the higher orders) using a higher order focus is not anoption with present detector efficiency (see section 5). In practice, this meansthat the resolution is limited by nanofabrication. It is difficult to make verysmall free-standing zones. For this reason, experiments have been done on aso-called atom sieve zone plate configuration. The atom sieve is a zone platesuperimposed with a hole pattern. The fabrication limit is now determinedby how small free-standing holes can be made, rather than by how smallfree-standing zones can be made. In fact, the resolution limit will be evensmaller than the smallest free-standing hole, because the design can be madeso that a hole covers two zones and the resolution limit remains the widthof a zone ∆r. The idea is adapted from photonics [91]. The first focusing ofhelium atoms using an atom sieve was done in 2015 [92] see also [93]. As afinal remark we can mention that it has been shown that the Beynon Gaborzone plate performs similar to a Fresnel Zone Plate [94]. The Beynon Gaborzone plate was previously cited in the literature as having a higher intensityin the first order focus that the Fresnel zone plate, however this turned outto be an artifact due to lack of sampling nodes.

4. Contrast properties

To the best of our knowledge the first paper dedicated to the conceptof contrast in SHeM was published in 2004 by MacLaren and Allison. It

26

discusses what contrast mechanisms are to be expected on the basis of thetheory of helium scattering [3].

The general theory of helium scattering has been treated in a range ofbooks and review articles, see for example [11, 10, 12, 13]. Unlike electrons,X-rays and neutrons which all interact with the core electronic cloud andatomic nuclei in the sample, thermal helium atoms scatter off the outermostelectron density distribution at the sample surface. The classical turningpoint for helium is a few Angstroms above the surface [95]. It is no surprisetherefore that the helium beam is very sensitive to surface defects such asadatoms, vacancies and atomic steps. Experimental results on metal surfaceshave shown that a defect coverage (defined as the ratio between the number ofadparticles and the number of surface atoms, both per unit area) of << 1% ofa monolayer can be detected [96, 97, 98]. The helium specular intensity (seebelow) decreases as a function of defect coverage, similarly to how a beamwhich crosses a gas-filled scattering cell has its centre line intensity reducedby collisions with gas atoms. The lost intensity turns into incoherent, diffuseintensity. This analogy allows the introduction of the concept of an effectivecross section for defects. The cross section of a single adatom as seen by

helium is typically 100 A2

which exceeds by far the atomic diameter. Even

for hydrogen, the cross section is estimate to be of the order of 10 A2

[99].To understand these large cross-section values, it is necessary to analyze

the scattering mechanism and in particular the helium-surface interactionpotential. This interaction can be separated into a short range repulsivepart, due to the overlapping of the electron densities of helium and the surfaceelectron density, and a long range attractive part, due to the van der Waalsinteraction. The repulsive part taken on its own, gives a cross section ofthe order of the atomic size, but including the attractive interaction whichmodifies the atom trajectories already far from the surface, increases theestimated cross section value to reach the experimentally measured values.As the coverage increases the effective cross sections of different defects startto overlap [100, 101].

The main different helium scattering processes that can occur are illus-trated in Figure 8. The first major distinction is between elastic and inelasticscattering. In the case of elastic scattering, the energy of the helium atomis unchanged during the scattering process. In inelastic scattering an energyexchange with the surface takes place through phonon creation or annihila-tion.

27

Specular scattering is elastic scattering, where the outgoing scattering an-gle is equal to the incident scattering angle. In the case where the roughness(variation in slopes) is on a length-scale bigger than the instrument resolution(focused spot size), the direction of the specularly scattered beam will vary.This is referred to in the SHeM literature as topographical contrast. In theextreme case, when the surface is so rough on the atomic level that it acts as aperfect elastically diffuse scatterer (see section 4.1) the reflected signal will beindependent from the incident beam direction, but still depend on the local,average surface normal. This is also referred to as topographical contrast.Roughness on the atomic level can occur through the presence of atomic de-fects, as discussed above. In the intermediate case, where the roughness issmaller than the instrument resolution but the surface is not a perfect dif-fuse scatterer, the specularly reflected beam will broaden. This broadeningprovides a measure for the roughness variation down to the scale of the wave-length of the helium atoms (Angstrom scale). This broadening effect has beenreferred to in the SHeM literature as sub-resolution contrast [102]. It pro-vides a unique method for fast, large area evaluation of nano-coatings [103].

As mentioned above the helium atoms have a wavelength on the Angstromscale, which is comparable to the atomic spacing in materials, so if the sub-strate is crystalline with a corrugated surface electron density distributionand reciprocal lattice parameters matching the k-vector component of thehelium atom parallel to the surface, elastic scattering can occur in the formof diffraction. Such diffraction contrast in SHeM was observed for the firsttime in 2020 [104], through imaging of a Lithium Fluoride crystal sample.Elastic scattering can also occur as resonant state scattering, also referredto as selective adsorption resonance, which occurs when the helium atom istrapped in the helium-surface interaction potential, however, this is generallya rare phenomena and has not been considered as a contrast forming processin SHeM up till now.

Finally, and not shown in the figure, we have the case where a surfaceis very rough relative to the wavelength of the atoms or has a deliberatelyimposed high aspect ratio structure. Here the atoms may undergo more thanone (elastic or inelastic) collision with the surface, which gives shadowingeffects. Multiple scattering contrast is described in [85], see also [86]. In theextreme case, when the atoms are thermally equibrilated with the surfacethrough the multiple scattering, the scattering profile will be spatially similarto that of a perfectly elastically diffuse scatterer, see section 4.1.

Inelastic helium scattering has been investigated for many years using so

28

called time of flight experiments, where the beam is chopped into short pulsesand the creation and arrival time of each pulse measured, so that the timeof flight (TOF) for each pulse can be converted into energy of the atoms andthus used as a measure for energy transfer with the surface - annihilationor creation of phonons. So far, however, no SHeM has been equipped withTOF.

For inelastic scattering, we distinguish between the single phonon andmulti phonon regimes, also referred to as the quantum and classical regimes.In the single phonon regime, the helium atoms excite or de-excite individ-ual phonon vibration modes. The single phonon regime occurs when singlephonon annihilation or creation is the dominant inelastic process and theprobability of exciting two or more phonons is small. In the multi phononregime several phonons are excited at the same time. This situation occursif the vibration energies for the surface molecule charge oscillations are muchlower than the energy of the incident helium atoms (the helium atoms seethe surface molecules as “floppy”). In this case there will not be discreteexcitations. Thermal vibrations of the surface atoms leads to an increase inmultiphonon scattering with temperature.

Inelastic scattering will lead to a loss in the elastically scattered signal.The intensity loss in the multiphonon regime I/I0 is described by the De-bye–Waller factor (DWF). The Debye-Waller factor was first introduced inX-ray scattering. For helium scattering it has the form (note the temperaturedependence) [105]:

I

I0

= e−24mT (Eicos

2θi+D)

MkΘD2 (20)

where Ei is the incident energy of a helium atom, m the mass of a heliumatom, M the surface atomic mass, θi the incident angle of the beam on thesurface and T the surface temperature and ΘD the Debye temperature, Dis the well depth of the helium surface interaction potential and k is theBoltzmann constant.

Equation 20 shows that inelastic scattering offers the possibility of chemicalcontrast, since different chemical compounds on the surface will lead to dif-ferent surface atomic mass, Debye temperature and well depth of the heliumsurface interaction potential. The first indication of chemical contrast stemsfrom 2015 when Barr et al. published the 4 SHeM images shown in fig-ure 9 [105]. They suggest that the remarkable contrast difference one observesin the images is due to the fact that different chemical elements (different

29

metals) are being imaged. It is argued that since helium can probe subsur-face resonances, chemical contrast can be provided even in the presence ofmultiple adsorbate layers. As an argument that the contrast is truly chemicaland not sub-resolution contrast caused by differences in surface roughness,the SHeM images are compared with AFM images. It is argued that the ob-served SHeM contrast does not follow the root mean square roughness trendin the AFM data. One may make the remark here, that roughness is in trutha spectral density function and determined by the ”ruler” used to measure it.For AFM this is the tip diameter - several nanometers, for SHeM the wave-length of the helium atoms - less than one nm. Thus one cannot necessarilyexpect the roughness measured with the two methods to be comparable.

In reality several contrast mechanisms will often be at play at the sametime. An interesting approach for exploring contrast mechanisms is foundin [106], where imaging has been done using a helium beam seeded withArgon. Similarly in [107] imaging using a helium beam seeded with Kryp-ton is explored. Seeded helium beams is a well established technology, usedamong others for thin film deposition, see for example [108]. In a microscopycontext the seeded beam technique makes it possible to obtain images si-multaneously with different atomic species of the same energy. In principlethis should make it possible to separate the different contrast mechanismsat play since, using equation 20 with different masses, m. In practice it isnot quite so simple because the interaction potential with the surface, andthereby the well depth, D will also vary. It should also be noted that theseeded beam imaging cannot be used in the zone plate configuration, sinceatoms with different masses at the same energy will have different de-Brogliewavelengths.

Exploration of contrast mechanisms in SHeM will no-doubt remain anintense research field in the future, just as is the case for other microscopytechniques.

4.1. Contrast modelling

So far theoretical modelling of contrast properties has focused on topo-graphical contrast only. Three different approaches have been used: Onemodel assumes perfectly diffuse elastic scattering (Lambertian scattering),a second model (Knudsen flux scattering) assumes perfectly diffuse inelasticscattering, with the scattered atoms equilibrated to the surface temperaturethrough multiple scattering. The third model assumes specular scatteringfrom individual slopes. The two first models have the same spatial scattering

30

Figure 8: Illustration of the different processes for the scattering of He atoms on a surface.For crystalline surfaces diffraction is included. The helium atom scatters off the electrondensity distribution, indicated as red lines, without any penetration into the bulk. Selec-tive adsorption refers to the trapping of a helium atom in the helium surface interactionpotential. Here λi and λf denote the wavelength of the incident and scattered heliumatoms, respectively. Inelastic scattering leads to a wavelength change, figure reproducedfrom [11].

distribution. The third model will approach the two others with increasingsurface roughness.

The two first publications of theoretical methods for calculating reso-lutions in SHeM’s assume Lambertian reflection for modelling the scatter-ing. [81, 76]. The term Lambertian reflection is taken from light optics, andcorresponds to scattering from a perfect, diffuse reflector. The scattered lobehas a cos θ spatial distribution with respect to the surface normal. The lightdoes not change its wavelength (energy) during scattering. In other words,the scattered lobe is independent of the energy and angle of the incidentbeam.

The second scattering model is Knudsen flux scattering, which has thesame cosθ scattering distribution as Lambertian reflection [109], see also [104].There is a fundamental difference however, between Lambertian reflectionand Knudsen flux scattering. In Lambertian reflection the light does notchange its wavelength (energy). This is not the case for the Knudsen fluxscattering. Knudsen scattering is the scattered (desorbed) distribution, whenthe incident beam is totally adsorbed on the surface into the physisorptionwell, and then remains in the well long enough to equilibrate to the surface

31

Figure 9: SHeM images showing the University of Newcastle logo in different metals on asilicon substrate. Clockwise from top left: a) gold, b) nickel c) platinum and d) chromium.Scale bar, 50 µm from [105].

32

temperature, and then ultimately leave the surface via desorption [110].The conditions for obtaining what we refer to as Knudsen flux scatter-

ing have undergone an interesting debate. Initially, the Knudsen flux wasthought to be the flux of particles that would pass through an imaginary flatplane placed in an equilibrium gas. However, this derivation was shown to beflawed by Wenaas [111]. In 2004 Feres and Yablonsky showed that Knudsenscattering was one17 of the expected results of a random billiard model forgas-surface interactions. This remains as one of the most convincing expla-nations for Knudsen scattering [112].

The cos θ distribution is used in [113]. Here the scattering is simplylabelled as diffuse scattering. It is not clear whether the Lambertian or theKnudsen flux scattering is referred to, however the result is the same asexplained above.

The last approach has been to model the scattering from rough surfacesas elastic scattering from a surface consisting of a distribution of slopes,obtained from independent AFM images [103]. It should be noted that inthe study referred to here, the samples imaged were macroscopically flat andthe explicit aim was to investigate the roughness on the (sub)-nanometerscale. A further extension is presented in [85] where multiple scattering isincluded in the modelling of images of samples with high aspect ratio.

5. Detection

Detection remains the single biggest challenge in neutral helium mi-croscopy. The big advantage of the technique - the inertness, low energyand surface sensitivity of the helium probe is its biggest disadvantage whenit comes to detection. Up till now three types of neutral helium detectors havebeen used and/or investigated for SHeM experiments: i) Pitot-tube detectors- an accumulation (stagnation) detector, where the pressure increase from thehelium flow into a small chamber is measured with a pressure gauge [39, 89](electron bombardment without mass selection). ii) electron bombardmentdetectors with mass selection [114, 115, 116, 117, 118, 119, 120, 121, 122, 106,123], and iii) field ionisation detectors [124, 125, 126, 127, 128]. Bolometers[129] have been used extensively in helium atom scattering experiments andphoton resonance has been applied to ionize helium [130, 131], but theseapproach have not been used in SHeM so far.

17But not the only one, other distributions are also possible.

33

Field ionsation detection is in principle a very attractive method, becauseit offers the possibility of extreme spatially resolved detection. The potentialof field ionisation is demonstrated in helium ion microscopy, which uses fieldionisation to generate a helium ion source, spatially confined to one ionizingatom. In an early helium microscope design proposal the sample is broadlyilluminated and a mirror focuses the reflected beam onto a field ionisationdetector [132]. So far a SHeM with field ionisation detector has not beenbuilt. The main reason for this is that the field ionisation probability isstrongly dependent on the velocity of the helium atoms and so would requirea strongly cooled beam to achieve a reasonable detection efficiency [126, 127]

Up till now all SHeMs have used electron bombardment detectors. He-lium has the highest ionisation potential of all species: around 24.6 V18. Akey component in a helium electron bombardment detector is therefore theioniser. Here, electrons are emitted from a negatively biased filament andaccelerated by an acceleration voltage, which must be greater than 24.6 V,towards the helium beam. Positive helium ions are then created throughcollisions with the high-energy electrons.

Once the helium atoms have been ionised, they need to be detected. Inthe simplest configuration this is done with a so-called Pitot-tube setup, usedamong others in [39, 89] for microscope characterisation experiments. Thehelium beam goes through a narrow tube into a small unpumped chamber.The intensity of the helium beam is then measured by recording the pres-sure increase in the small volume, see [80] for a description of a practicalimplementation. The Pitot-tube detector is very inefficient and can in prac-tice only be used for transmission experiments, where the recorded beamintensity will be high.

A much more efficient detection is achieved by mass separation: designedto select only those ions that interest us (helium ions coming from the beam).In SHeM (and HAS) this is often done using magnets [133, 123] rather thanthe quadruple mass filters typically used in commercial residual gas analysers(mass spectrometers) [134], because the magnets yield higher recorded inten-sities for helium. A magnet-based detector was used for the first (transmis-sion) SHeM images [37]. A description of the design can be found here [114].The helium atoms are directed from the ioniser to the mass separation stageand from the mass separation stage to the signal multiplier using ion optics

18https://physics.nist.gov/PhysRefData/Handbook/Tables/heliumtable1.htm

34

[106, 135, 123]. The signal multipliers used in SHeM are electron multipliers,typically tube-based multipliers known as channeltrons [136, 137].

A lot of time and energy has been spent on increasing the efficiency ofneutral helium detectors. Especially promising are detector systems basedon solenoidal ionisers, with recent work reaching an efficiency of as muchas 0.5% [123] - the highest obtained to date and around three orders ofmagnitude higher than for the detector used in the first helium microscopyexperiments [114]. Another promising development is a recent frameworkaimed at optimising the balance between signal and temporal response inneutral helium detectors. The basic idea is to use adjustable stagnation toobtain a larger helium signal, with a reported signal improvement of 27%[138].

5.1. Signal to Noise Ratio

Unfortunately a high ionisation efficiency for helium is not the only re-quirement for a powerful SHeM instrument. An equally crucial parameter isthe signal to noise ratio, which sets a limit for the smallest signal that can bedetected in a given measurement time. For electron bombardment detectors,the only detector type used in SHeMs so far, as mentioned above, there aretwo factors that contribute to the noise:

Firstly there is a contribution of ions from other species present in thebackground gas. Species such as H2, H2O, CO and CO2 will always bepresent, because the vacuum is not perfect. These species all have a muchlower ionisation potential than helium. Most of the ions generated will bewithheld by the mass filter, but in the case of for example triple ionisationof carbon, they will be mass selected. Multiple ionisation can be stronglyreduced by keeping the energy of the ionization energy as low as possible,a good vacuum also helps in general, but even so a contribution from thebackground gas cannot be completely prevented.

Secondly, there will be a background contribution from the helium probeitself. The part of the helium beam which is not directly reflected into thedetector by the sample, will be scattered in the rest of the chamber andreflected off the walls, thus creating an additional background of helium inthe chamber. A fraction of this helium background will reach the detector.Because this is a background of helium, it will be detected with the sameprobability as the real helium signal. Praxis has shown that this heliumbackground usually is the dominating contributing factor to the noise inSHeMs. The magnitude of the background will depend on factors such as

35

Source

SupersonicExpansion

Sample

plan

e

Detector

Zone plate

Skimmer

Nozzle

CollimatingAperture

Figure 10: Simplified diagram of the zone plate microscope setup in reflection

pumping speed and detector opening area. It can be reduced by using amodulated beam (chopped beam) as has been demonstrated with many othertechniques, however so far this has not been implemented in SHeM. This isa very hard task since the requirement of high efficiency for the detector isgenerally obtained at the expenses of the response time which is lengthened,whereas modulation techniques require a relatively fast time response.

6. Optimal microscope configurations

The difficulties associated with detecting neutral helium atoms have promptedseveral researchers to try to optimise the design of helium microscopes to ob-tain a maximum beam intensity for a given resolution.

To date, there are four papers that aim to optimise the microscope designusing a theoretical framework for the beam intensity. The first paper from2016, written by Kaltenbacher [82] presents an approach to optimise a mi-croscope composed of a pinhole and two zone plates. However, Kaltenbacherdoes not consider the dependency of the beam centre-line intensity with theskimmer radius, rendering his approach not reliable in terms of the intensity.The next two papers from 2016 and 2018 [81, 50], by Salvador et al. presentanalytical approximations for calculating the optical configurations for pin-hole and single zone plate SHeMs in terms of resolution and intensity. Inaddition, the system is also solved numerically. The zone plate configurationoptimised can be found in Fig 10. The pinhole configuration has alreadybeen shown in the introduction, Fig. 5.

The last paper on microscope optimisation by Bergin et al. from 2019 [83]also presents optimisations of a pinhole and a single zone plate microscope

36

Skimmer radius (x_s in Bergin et al.)

a (r_s in Bergin et al.)

Sr

PHr

Sample plane

WD (f in Bergin et al.)

Pinhole

Supersonic

Expansion

Axis of

cilindrical

symmetryNozzle

Quitting surface

δx

Figure 11: Sketch showing the pathway of the beam onto the sample for a pinhole micro-scope. The figure illustrates how the beam is limited by the skimmer in the Salvador etal. approach. The geometrical optics image of the skimmer is projected onto the sampleplane through a pinhole, giving an image of the skimmer with radius δ.

including numerical simulations. It reaches the same qualitative conclusionson beam design as the two previous papers. The differences in the approachesof Bergin et al. and Salvador et al. are that Salvador et al. model the sourceusing the full Sikora model (eq. (4) in this paper) whereas Bergin et al.use a simplified approximation of the Sikora model (eq. (13) in this paper).Both approaches models the beam as a Gaussian distribution with a stan-dard derivation σ corresponding to the skimmer radius, but Salvador et al.includes an additional limitation of the beam by the skimmer diameter asin geometrical optics, see Fig. 11. Furthermore Salvador et al. use deriva-tion to solve the optimisation problem, whereas Bergin et al. use Lagrangemultipliers.

Both Salvador et al. and Bergin et al. provide analytical expressions forthe optimal pinhole size in a pinhole microscope configuration. Salvador et al.produce a solution valid for any working distance (WD), while Bergin et al.implicitly assumes WD � a, where WD is the microscope working distance(distance between pinhole and sample plane, f in the original Bergin et al.paper) and a is the distance between the skimmer and the pinhole (rs in theoriginal Bergin et al. paper), see Fig. 11.

Salvador et al. obtain the following solution for the optimal pinhole radiusroptPH (eq. 18 in the original paper [81]).

roptPH =ΦPH · a

2K(a+WD)

WD�a≈ ΦPH

2K. (21)

where ΦPH is the Full Width at Half Maximum of the beam at the sample

37

plane (the resolution, see section 3) and K =√

8 ln(2)/3. We see that thediameter of the pinhole is always smaller than the Full Width Half Maximumof the beam at the sample plane. For the case WD � a the solution becomesindependent of both WD and a.

Bergin et al. obtain the following expression for the optimal pinholediameter, doptPH , (equation (25) in the original paper [83]):

doptPH =√

6ΦσPH ≈ 2.45Φσ

PH . (22)

Where ΦσPH is the standard deviation of the helium beam at the sample

plane. Since both approaches model the beam as a Gaussian distribution wehave ΦPH = 2

√2 ln 2Φσ

PH . The solution of Salvador et al. for WD � a interms of Bergin et al. parameters thus becomes:

doptPH = 2√

2 ln 2ΦσPH/

√8 ln(2)/3 =

√3Φσ

PH ≈ 1.73ΦσPH (23)

For a zone plate configuration analytical solutions are harder to obtain. Sofar, only one has been published, obtained under several assumptions listedin [76]. Given these assumptions, the optimal distance between the skimmerand the zone plate a, which corresponds to the solution of the following cubicequation:

a3 + 2a2(RF −

√3Γrzp

)+ aRF(RF − 4rzp

√3Γ)

= rzp

√3ΓR2

F

[2S2Φ′2 + r2

zp(Γ− 1)

S2Φ′2 − 0.5r2zp

]. (24)

Where Γ ≡ 13

(2∆rλ

)2is a constant of the problem which gives the rel-

ative size of the smallest zone, ∆r, of the zone plate with a given radiusrzp compared with the average wavelength of the beam, usually Γ � 1. Sis the speed ratio in eq. (4). RF is the radius of the quitting surface and

Φ′ =

√(ΦZPK

)2 − σ2A is the corrected focal spot size (the focal spot size minus

the diffraction term given by the smallest zone).The work done on optimal SHeM configurations has had major impact in

microscope design. Most importantly, it has proven that for high resolutionsthe zone plate microscope provides higher intensities than the pinhole micro-scope (see Fig. 12). This is not an obvious insight, given that only around12.5% of the beam incident on the zone plate enters the focused beam spot

38

Figure 12: Plot of the optimised beam intensity (flux) versus beam standard deviation (σ)at the sample plane. σ is a measure for the resolution, Φ, which is defined in section 3as Full Width Half Maximum of the beam at the sample plane. For a Gaussian beam wehave: Φ = 2

√2 ln 2σ. We see that for lower resolutions the pinhole microscope performs

better, but as the resolution improves it is outperformed by the zone plate microscope. Forthe configuration optimised here resolutions better than around 200 nm are only possiblewith a zone plate microscope. Figure reproduced from [83], where details regarding theoptimisation parameters can also be found.

(see section 3), whereas 100% of the beam that passes through the pinholecontributes to the beam spot. Furthermore, the work has shown that thefirst SHeM designs were sub-optimal. In the case of the zone plate micro-scope the intensity could be increased by a factor of 7 [76], and in the caseof the pinhole microscope by a factor 1.75 [81]. In practice the work hasalready led to new microscope designs using bigger skimmers and smallerpinhole-skimmer distances.

6.1. Microscopes with micro-skimmers

Initial designs of helium microscopes used skimmers as small as techni-cally feasible (a few µm or less). This was motivated by the desire to obtainfocal spots as small as possible and micro-skimmers seemed the best wayto go in the zone plate/focusing mirror set up. The first supersonic He-lium beams with micro-skimmers were created by Brown et al. in 1997 [53].Micro-skimmers are made by controlled drawing of glass tubes produced ac-

39

cording to techniques developed for patch-clamp probing of cells. Brown etal. observed a broadening of the speed ratio in micro-skimmers comparedto standard skimmers and suggested that this was due to geometrical im-perfections and/or imperfections at the lip edge. It was recently shown thatit is possible to obtain speed ratios from micro-skimmers similar to thoseobtained from standard skimmers [51].

Eventually it became clear that the centre-line intensity from micro-skimmers was a limiting factor for the signal intensity in the imaging spot,and a systematic study of the influence of the skimmer size on the centre-line intensity was conducted [50], using skimmer diameters of 4, 18, 120 and390 µm diameters and in addition two flat apertures with diameters 5 and100 µm. Some further measurements using a 50 µm diameter skimmer canbe found in [139]. The results obtained from [50] was one of the incitementsfor the work on microscope optimisation discussed above. Here it is con-firmed that the dependency of the centre-line intensity with the skimmerradius plays an important roles for the imaging spot intensity [81, 76, 83].

Since then, new SHeM designs of both pinhole and zone plate config-uration, use skimmers as big as possible given available pumping speed incombination with collimating apertures in front of the skimmer, taking intoaccount skimmer interference at large Knudsen numbers as mentioned inSec. 2.2.3. This has the additional advantage that it enables fast resolutionchange by switching between different collimating apertures in situ [89].

7. 3D imaging

Perhaps the most interesting perspective for SHeM is the potential to dotrue-to-size 3D imaging on the nanoscale: a nano-stereo microscope. The first3D helium microscopy images were obtained by Myles et al. [140] in 2019.The 3D images were obtained by measuring the displacement of particularpoints of a 2D image when the sample was rotated by a given known angle,so called stereophotogrammetry

To avoid having to map individual sample points in different images,Lambrick and Salvador et al. in 2021 developed a theoretical framework forHeliometric Stereo, an extension of Photometric stereo to helium microscopy[86]. The difference between stereophotogrammetry and photometric stereois that in photometric stereo the 3D structure is recovered using variationsin the intensity signal rather than geometrical displacement of the imagedpoints. Due to the fact that helium microscopy images are taken in an

40

ortographic projection and constructed by imaging the sample point by point,photometric stereo can be translated to helium in an easy implementationas the image acquisition conditions are highly controlled.

Heliometic stereo is based on the fact that the intensity signal measuredin detectors placed in different angles will be different and depend on thetilting angle of the imaged surface. This dependency with the scatteringdistribution is both a curse and a blessing: on the one hand, for heliometricstereo to be implemented straightforwardly one must know the distribution.On the other hand, however, heliometic stereo sets the perfect conditions forestimating this distribution when it is unknown as it samples it for a varietyof scattering angles [85, 113, 86].

8. Supplementary Information: An overview of published SHeMimages and PhD thesis related to SHeM development

In this section we present an overview of, to the best of our knowledge,all SHeM images published in the scientific literature so far. The overview ispresented as a chronological table (see table 1). In addition we present a tableof, to the best of our knowledge, all PhD theses related to the topic of SHeM(see table 2). We have included links for download where available. Notethat master theses and other student reports have not been included. Wehave cited PhD thesis in the main text in the cases where we have found thatthey contain relevant work, which has not been published in peer reviewedjournals.

Table 1: Table of SHeM images published in the scientificliterature so far.

Ref. Imaged object Imaging beam spot sizeor pinhole diameter

[37] • hexagonal copper grating (transmission) 3µm and 2µm[40] • carbon holey foil (Quantifoil®, R2/1) (transmission) < 2µm and ∼ 2.3µm[38] • carbon holey foil (Quantifoil®, R2/1) (transmission) < 2µm and ≤ 1µm[2] • crushed high-field NdFeB magnet 1.5µm

• uncoated pollen grain 1.5µm[141] • aluminium sample

•TEM grid, back side, with glass microspheres

41

[46] • uncoated Crocosmia pollen grains 0.35± 0.05µm• debris cluster 0.35± 0.05µm• silicon wafer 0.35± 0.05µm

[47] •Lithium Fluoride (LiF) crystal and LiF debris 0.35µm• IC test pattern, low-k dielectric on Si 0.35µm• crumpled Au film on mica 0.35µm• crumpled mica 0.35µm• line pattern test sample, low-k dielectric on Si 0.35µm• crumpled multilayer graphene 0.35µm•Crocosmia pollen grain 0.35µm

[49] • broken copper TEM grid 5± 1µm• polymer bonded explosives 5± 1µm• tin spheres on carbon 5± 1µm

[142] • butterfly wing (Tirumala hamata) pinhole ∅ = 5µm•TEM grid adhered to Si wafer pinhole ∅ = 5µm

[143] • honey bee wing (Apis mellifera) 5.4µm• gold logo on Si 5.4µm• gold, nickel, platinum & chromium

logo on Si,respectively5.4µm

[102] • hexagonal TEM grid suspended offstainless steel

6.9± 0, 2µm

• central portion of a silicon nitridex-ray window

6.9± 0, 2µm

• sugar crystal (sucrose)adhered to a carbon dot

6.9± 0, 2µm

• 3D printed step sample,resin (RSF2-GPCL-04)

6.9± 0, 2µm

• 3D printed angled planes,resin (RSF2-GPCL-04)

6.9± 0, 2µm

• eye of a honey bee (Apis Melifera) 6.9± 0, 2µm[113] •TEM grid tick mark 3.5µm[140] • 3D printed sample, resin (RSF2-GPCL-04) 6.9± 0, 2µm

• pyrite crystal 6.9± 0, 2µm• trichomes on Mouse-ear Cress

(A. thaliana.) rosette leaf6.9± 0, 2µm

42

• dermal denticles on dorsal skin ofPort Jackson shark(Heterodontus portusjacksoni)

6.9± 0, 2µm

[138] • silicon nitride membrane pinhole ∅ = 5µm• australian Emerald Tip Beetle

(Anoplognathus chloropyrus)pinhole ∅ = 5µm

[104] • cleaved LiF crystal pinhole ∅ = 1.2µm[85] • trenches milled into Si wafer pinhole ∅ = 2µm

• porous scaffold, AlvetexTM (polystyrene) pinhole ∅ = 2µm[107] •MoS2 films grown on SiO2/Si substrate 23µm

Table 2: Table of PhD theses related to the topic ofSHeM.

Author name Published, Title, link (if available)

Bodil Holst 1997, University of Cambridge, UK[144] Atom Optics and Surface Growth Studies

using Helium Atom Scatteringethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.604194

Stefan Rehbein 2001, Georg-August-University Gottingen, Germany[43] Entwicklung von freitragenden nanostrukturierten

Zonenplatten zur Fokussierung undMonochromatisierung thermischerHelium-Atomstrahlencuvillier.de/de/shop/publications/3768

Donald Angus Maclaren 2002, University of Cambridge, UK[132] Development of a single crystal mirror

for scanning helium microscopyrepository.cam.ac.uk/handle/1810/251834

Rob T. Bacon 2007, University of Cambridge, UK[145] Aspects of atom beam microscopy

and scattering from surfacesethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596236

Ann Elizabeth Weeks 2008, University of Cambridge, UK[33] Si(111) atom-optical mirrors

43

for scanning helium microscopyethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.611911

Peter Thomas Hustler-Wraight 2008, University of Cambridge, UK[139] Aspects of atom-surface interactions:

considerations for microscopyethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.611936

Kane Michael O’Donnell 2009, University of Newcastle, Australia[146] Field ionization detection for atom microscopy

hdl.handle.net/1959.13/802939Andrew Robert Alderwick 2010, University of Cambridge, UK[117] Instrumental and analysis tools for

atom scattering from surfacesethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608817

Thomas Reisinger 2011, University of Bergen, Norway[45] Free-standing, axially-symmetric diffraction gratings

for neutral matter-waves:experiments and fabricationbora.uib.no/bora-xmlui/handle/1956/5039

Sabrina Daniela Eder 2012, University of Bergen, Norway[1] A neutral matter-wave microscope (NEMI):

design and setupbora.uib.no/bora-xmlui/handle/1956/23887

David Matthew Chisnall 2013, University of Cambridge, UK[147] A high sensitivity detector

for helium atom scatteringethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.607777

Matthew Gordon Barr 2015, University of Newcastle, Australia[148] Imaging with atoms:

aspects of scanning helium microscopyhttp://hdl.handle.net/1959.13/1312654

Gloria Anemone 2017, Universidad Autonoma de Madrid, Spain[149] Development of Graphene Atomic Mirrors

for Neutral Helium Microscopyrepositorio.uam.es/handle/10486/681667

Ranveig Flatabø 2018, University of Bergen, Norway[150] Charged particle lithography for the

fabrication of nanostructured optical elements

44

bora.uib.no/bora-xmlui/handle/1956/23609Matthew Bergin 2018, University of Cambridge, UK[106] Instrumentation and contrast mechanisms

in scanning helium microscopyrepository.cam.ac.uk/handle/1810/290645

Adam Joseph Fahy 2018, University of Newcastle, Australia[87] A practical consideration of

scanning helium microscopyhttp://hdl.handle.net/1959.13/1397850

Joel Martens 2019, University of Newcastle, Australia[151] A prototype permanent magnet solenoidal ioniser

for the newcastle scanning helium microscopehttp://hdl.handle.net/1959.13/1422721

Adria Salvador Palau 2021, University of Bergen, Norway[152] On the design of Neutral Scanning Helium Atom

Microscopes (SHeM) - Optimal configurations andevaluation of experimental findings

9. Conclusion and Outlook

In this paper we present an overview of the development of Neutral he-lium atom microscopy (SHeM) from the beginning and up to this day. Newdevelopments makes the future look promising: The exciting perspective oftrue to size 3D imaging, the recent demonstration of sub-resolution contrastwhich allows fast characterisation of Angstrom scale roughness over large ar-eas and the improvements in detector technology, just to mention a few. Allof this taken together with the developments in nanocoatings and micro andnanostructuring applications makes it very probable that SHeM will find itsuse in a larger research and technology community within the next few years.The success of SHeM is likely to depend, at least to some extend, on furtherinvestigations of contrast mechanisms. Therefore, the next instrumental de-velopment step for SHeM should ideally include the possibility of chopping(pulsing) the beam so that energy resolved measurements (Time of Flight)experiments can be performed. This would allow the different contrast con-tributions to be separated and analysed independently. It would also enable

45

strategies for reducing the helium background, thus improving the signal tonoise ratio which would increase the sensitivity of the instrument. Choppedbeam experiments do however, require fast response time of the detector,which lowers the efficiency. For measurements of structures of known com-position it may in some cases suffice to characterize the scattering profileindependently using HAS on a flat reference surface. All new instrumentsshould be equipped with a simple sample heating, so that water and othercontaminates can be removed in order to obtain more contrast informationdirectly from the sample material.

10. Acknowledgement

We thank William Allison, Paul Dastoor, Daniel Farias, Holly Hedgeland,Donald McLaren and Andy Jardine for useful discussions and feedback. BHacknowledges support of SHeM development from the European Commissionthrough the two collaborative research projects INA, FP6-2003-NEST-A,Grant number 509014 and NEMI, FP7-NMP-2012-SME-6, Grant number309672

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